Definitions
from The Century Dictionary.
- In the ratio of a number to the next lower number.
from the GNU version of the Collaborative International Dictionary of English.
- adjective (Math.), obsolete Of or pertaining to a ratio when the excess of the greater term over the less is a unit, as the ratio of 1 to 2, or of 3 to 4.
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- adjective mathematics, obsolete Of a natural number, being larger than another natural number by a
unit fraction of that smaller number. - adjective mathematics, music Pertaining to a ratio of any whole number to the next below it (i.e. , etc.).
Etymologies
from Wiktionary, Creative Commons Attribution/Share-Alike License
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Examples
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The ratios which govern the basic musical intervals (2: 1, 4: 3, 3: 2, 9: 8), all belong to a type of ratio known as a superparticular ratio -- roughly speaking, ratios of the form (n + 1): n.
Archytas Huffman, Carl 2007
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The ratios in Archytas 'diatonic and enharmonic tetrachords are indeed superparticular, but two of the ratios in his chromatic tetrachord are not superparticular (32: 27 and 243: 224).
Archytas Huffman, Carl 2007
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Second, Ptolemy, who is our major source for Archytas 'tetrachords (A16), argues that Archytas adopted as a principle that all concordant intervals should correspond to superparticular ratios.
Archytas Huffman, Carl 2007
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Barker tries to save Archytas 'adherence to the principle that all concordant intervals should have superparticular ratios, but there is no direct evidence that he was using such a principle, and Ptolemy may be mistaken to apply it to him.
Archytas Huffman, Carl 2007
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Archytas made a crucial contribution by providing a rigorous proof that there is no mean proportional between numbers in superparticular ratio (A19) and hence that the basic musical intervals cannot be divided in half.
Archytas Huffman, Carl 2007
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Plato might well have welcomed a principle of concordance based solely on mathematical considerations, such as the principle that only superparticular ratios are concordant, but Archytas wanted to explain the numbers of the music he actually heard played.
Archytas Huffman, Carl 2007
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Page 262, Volume 3 that it was the perfect tuning, because both perfect and imperfect consonances were in simple ratios of the class n + 1/n, known as superparticular.
MUSIC AND SCIENCE CLAUDE V. PALISCA 1968
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For example, I've written pieces that generate harmonies from combination tones, and I've recently been inspired by Greg Scheimer's work to focus on epimores (i.e., superparticular ratios).
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